CN102183766B - Stratum chromatography method by synthetic aperture - Google Patents

Abstract

The invention provides a stratum chromatography method by synthetic aperture, comprising the following steps: first, performing the low frequency broadband signal pulse compression treatment to obtain the high resolution at deep dimension and enough stratum penetration properties; and then, performing synthetic aperture treatment on the sea water and seabed laying data with different sound speeds to obtain the high resolution at navigation dimension; at last, solving the fuzzy problem of the interface by the layering two-dimensional forward normalization post-processing, and further improving the resolution for the seabed stratum. The invention has the advantages that the technical invention successfully applies the synthetic aperture technique to the field of the stratum chromatography; the invention performs the seabed stratum chromatography by the synthetic aperture processing method which applies different sound speeds to different layer datas to improve the resolution of the stratum chromatography system at the navigation dimension; meanwhile, the invention performs layering two-dimensional forward normalization post-processing on the basis of the synthetic aperture treatment to further solve the fuzzy problem of the interface and improve the resolution of the stratum.

Description

A kind of synthetic aperture stratum chromatography method

Technical field

The invention belongs to seabed stratum detecting, ocean prospecting new technical field, mainly is a kind of synthetic aperture stratum chromatography method.

Background technology

Contain abundant mineral wealth in the ocean, it is quite important to Yu Haiyang prospecting (visiting oil, rock gas etc.) to understand the seabed stratal configuration; The ocean also is the platform that we carry out various marine activities simultaneously, understands the seabed stratal configuration and (builds seashore harbour, sea wall platform for oceanographic engineering; Undersea pipe-laying, tunnel are opened etc.), seabed threat detection (the submarine volcano distributed architecture is buried thunder layout etc.) is all most important.

Stratum, seabed chromatography is a geoanalytical techniques understanding seabed sedimentation sequence, stratum texture feature by corresponding method, means.Current the most frequently used be drill, sample analysis obtains formation information, but because the ocean complex situations, the emission low frequency penetrates sound wave, carries out the echo inverting then is large-scale seabed stratum chromatography best method.There is no in the world at present ripe stratum, seabed tomographic system, using commonplace is the shallow system of cuing open, the shallow systems face of cuing open away the dimensional imaging lack of resolution problem of navigating, to some little targets or meticulously layer texture can't differentiate, the key that therefore realizes stratum, seabed chromatography is the restriction of Gonna breakthrough Imaging Resolution.In the present invention's innovation, adopt synthetic aperture technique to carry out stratum, seabed chromatography, to improve it at the resolving power of dimension of walking to navigate, carry out simultaneously the rearmounted processing of layering two dimension forward direction normalization on the basis of synthetic aperture processing with further solution interface fuzzy problem and improve stratigraphic resolution power.Synthetic aperture technique is used stratum, seabed Image processing still belong in the world at present the first, have a lot of key issues to need to solve.Variation issue such as the velocity of sound in the stratum, refraction problems when sound wave penetrates between layering, and the seawater that causes of synthetic aperture stratum chromatography, seabed interphase fuzzy problem etc., these factors all will affect the gain output of synthetic aperture.Solve these key issues and will advance effectively the synthetic aperture technique range of application, creatively make it extend to chromatography field, stratum from traditional detection landform, landforms field.

Synthetic aperture stratum chromatographic technique is at first processed by the broad band low frequency compression of signal pulse and is obtained the depth dimension high resolution, and enough stratum penetration performances; Then different individual-layer datas being used the different velocities of sound carries out synthetic aperture processing and obtains away boat dimension high resolution; Further improve seabed stratigraphic resolution power by rearmounted processing of layering two dimension forward direction normalization at last.

Summary of the invention

Purpose of the present invention is just in order to overcome the deficiency of above-mentioned technology, and a kind of synthetic aperture stratum chromatography method is provided.

The present invention solves the technical scheme that its technical matters adopts: this synthetic aperture stratum chromatography method comprises that step is as follows:

(1), obtain the stratum echoed signal: launch the broad band low frequency signal, adopting the linear FM signal bandwidth is 1～15kHz, and the layering interfaces reflection echo of acquisition carries out processing by the full frequency band matched filtering;

(2), synthetic aperture stratum chromatography: adopt the vertically downward working method of broad beam transmitting/receiving of acoustic matrix, for stratum echo synthetic aperture processing, synchronization receives the echo of the arc-wave front of a solid, adopts conventional synthetic aperture algorithm to carry out the synthetic aperture focusing wave beam at signal processing method and forms processing;

(3), layering synthetic aperture processing: use the end tracking echo data is divided into two parts of seawater and seabed, then according to seawater, acoustic velocity value that the seabed market demand is corresponding are carried out synthetic aperture processing, to improve stratum chromatography resolving power;

(4), carry out rearmounted processing of layering two dimension forward direction normalization on the basis of synthetic aperture processing; Carry out respectively normalized for seawater, seabed, solve the very fast problem of stratum, seabed echo attenutation of different depth, tentatively suppressed the interface fuzzy problem that causes owing to synthetic aperture processing simultaneously, and raising stratigraphic resolution power, highlight stratum chromatography effect.

As preferably, adopt the combined transmit transducer, adopt the sequential firing mode: one group of transducer is launched first the LFM signal of 1kHz-5kHz, accounts for 1/3 of total pulsewidth launch time; And then the LFM signal of another group transducer emission 5kHz-15kHz accounts for 2/3 of total pulsewidth launch time.

As preferably, be adopted as time delay focused synthetic aperture disposal route, namely data after the matched filtering are represented ss (n, m) with discrete form, m, n represent to walk respectively boat dimension sample point and depth dimension sample point (m=1,2 ... M; N=1,2 ... N), then image output

$\mathrm{ff}(n,m)=\underset{i=1}{\overset{L_{\mathrm{SA}}}{\mathrm{\Σ}}}\mathrm{ss}(n+\mathrm{\τ}(n,i),m+i)---\left(2\right)$

L in the formula _SAFor the orientation to length of synthetic aperture, τ (i, n) is defined as the Delay Variation amount that the range migration curve causes

$\mathrm{\&tau;}(n,i)=\sqrt{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HSA00000430220700012.png"\; state="\{\{state\}\}">n</figure-callout>}}^2+[2f_s\&CenterDot;i\&CenterDot;d/c]}-n,i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;L_{\mathrm{SA}}---\left(3\right)$

Wherein d is that spacing is adopted in the space, and c is the velocity of sound, and [] expression rounds operation, carries out the sample interpolation operation for obtaining accurate delay in processing.

As preferably, seawater data in the echo of stratum are separated with the seabed data, it is used different acoustic velocity values carry out synthetic aperture processing;

● follow the tracks of and process seawater, seabed data separating at the end:

Obtain after the matched filtering data energy and integration in short-term

$\mathrm{Ess}(m,n)=\frac{1}{J}\underset{j=1}{\overset{J}{\mathrm{\&Sigma;}}}\left|\mathrm{ss}(m,n+j)\right|---\left(4\right)$

$\mathrm{EEss}\left(m\right)=\frac{1}{N}\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{Ess}(m,n)---\left(5\right)$

When Ess (m, n) 〉=0.707*EEss (m) declares N _s(θ)=n is the seabed constantly;

● the layering synthetic aperture processing:

Seawater after separating, the different velocity of sound data of seabed market demand are carried out synthetic aperture stratum chromatography, in synthetic aperture processing, form a fuzzy band near the interphase in seawater and seabed, this fuzzy band is by rearmounted normalized.

The effect that the present invention is useful is: the present technique invention successfully is applied to chromatography field, stratum to synthetic aperture technique.The synthetic aperture processing method that adopts different individual-layer datas to use the different velocities of sound among the present invention is carried out stratum, seabed chromatography, to improve the stratum tomographic system at the resolving power of walking the boat dimension; Carry out simultaneously the rearmounted processing of layering two dimension forward direction normalization on the basis of synthetic aperture processing with further solution interface fuzzy problem and improve stratigraphic resolution power.

Description of drawings

Fig. 1: the geometric relationship of stratum echo synthetic aperture processing;

Fig. 2: sonic velocity change Technologies Against Synthetic Aperture wave beam impact;

Fig. 3: layering synthetic aperture stratum Image processing flow process;

Fig. 4: cross-sectional data stratum, large tracts of land stratum tomographic results;

Fig. 5: the three-dimensional stratum imaging result of target is buried in the seabed.

Embodiment

The invention will be further described below in conjunction with drawings and Examples:

Adopt synthetic aperture technique to carry out stratum, seabed chromatography among the present invention, to improve the stratum tomographic system at the resolving power of dimension of walking to navigate, carry out simultaneously the rearmounted processing of layering two dimension forward direction normalization on the basis of synthetic aperture processing with further solution interface fuzzy problem and improve stratigraphic resolution power.Stratum, seabed chromatography is a geoanalytical techniques understanding seabed sedimentation sequence, stratum texture feature by corresponding method, means.Current the most frequently used be drill, sample analysis obtains formation information, but because the ocean complex situations, the emission low frequency penetrates sound wave, carries out the echo inverting then is large-scale seabed stratum chromatography best method.There is no in the world at present ripe stratum, seabed tomographic system, using commonplace is the shallow system of cuing open, the shallow systems face of cuing open away the dimensional imaging lack of resolution problem of navigating, to some little targets or meticulously layer texture can't differentiate, propose in the present invention synthetic aperture technique is applied to stratum, seabed chromatography to break through Imaging Resolution restricted problem.Synthetic aperture stratum chromatography method is at first processed by the broad band low frequency compression of signal pulse and is obtained the depth dimension high resolution, and enough stratum penetration performances; Then using the different velocities of sound for seawater, seabed individual-layer data carries out synthetic aperture processing and obtains away boat dimension high resolution; Deal with the interface fuzzy problem and further improve seabed stratigraphic resolution power by layering two dimension forward direction normalization postposition at last.

As shown in the figure, this synthetic aperture stratum chromatography method comprises that step is as follows:

1. obtain the stratum echoed signal

Emission broad band low frequency signal is to obtain enough stratum penetration performance and stratum chromatography resolving power.Adopting the linear FM signal bandwidth is 1～15kHz, and it is 5.3cm that the layering interfaces reflection echo of acquisition carries out processing acquisition theoretical resolving power by the full frequency band matched filtering.

Because the transducer technological problems is difficult to realize the large broadband of low frequency, here adopt the combined transmit transducer, for realizing broadband 1～15kHz work, adopt the sequential firing mode in this programme: one group of transducer is launched first the LFM signal (account for launch time total pulsewidth 1/3) of 1kHz-5kHz, and then the LFM signal of another group transducer emission 5kHz-15kHz (account for launch time total pulsewidth 2/3).

The broad band low frequency signal can produce strong reflection at the interface of strata division in the earth penetrating process, thereby obtains to comprise the stratum echoed signal of formation information, by it carries out the tentatively hierarchical information of inverting stratum media of matched filtering processing to echoed signal.

2. synthetic aperture stratum chromatography

In order to realize the stratum chromatography, adopt the vertically downward working method of broad beam transmitting/receiving of acoustic matrix, it and traditional side are swept the synthetic aperture working method and are had very big difference.For stratum echo synthetic aperture processing, synchronization receives the echo of the arc-wave front of a solid, and its geometric relationship is shown in Fig. 1 synoptic diagram.Sonar platforms is at position A place among the figure, it is perpendicular to any two point target P1 and the P2 of arc-wave front on the direction of walking to navigate, they equate (r1=r2) to the sound path that receives battle array, when platform moves to the B position, the sound path of these two targets still equates to receive (r1 '=r2 ') echoed signal in the direction of walking to navigate and still satisfy the para-curve focusing criterion.

$R=\sqrt{r^2+x^2}---\left(1\right)$

As seen, although being multiple goal, the stratum echo is superimposed, it is identical that but the duration curve of each reflectance target and conventional side are swept the time-delay relation curve that the synthetic aperture processing of mode obtains, so we still can use conventional synthetic aperture algorithm to carry out the synthetic aperture focusing wave beam to form and process on signal processing method.

This programme is adopted as time delay focused synthetic aperture disposal route, namely data after the matched filtering is represented ss (n, m) with discrete form, m, n represent to walk respectively boat dimension sample point and depth dimension sample point (m=1,2 ... M; N=1,2 ... N), then image output

$\mathrm{ff}(n,m)=\underset{i=1}{\overset{L_{\mathrm{SA}}}{\mathrm{\&Sigma;}}}\mathrm{ss}(n+\mathrm{\&tau;}(n,i),m+i)---\left(2\right)$

L in the formula _SAFor the orientation to length of synthetic aperture, τ (i, n) is defined as the Delay Variation amount that the range migration curve causes

$\mathrm{\&tau;}(n,i)=\sqrt{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HSA00000430220700012.png"\; state="\{\{state\}\}">n</figure-callout>}}^2+[2f_s\&CenterDot;i\&CenterDot;d/c]}-n,$ i＝1，2，…L _SA (3)

Wherein d is that spacing is adopted in the space, and c is the velocity of sound, and [] expression rounds operation.In processing, carry out rising the sample interpolation operation for obtaining accurate delay.

3. layering synthetic aperture processing

Seawater, sonic velocity change Technologies Against Synthetic Aperture processing gain impact in the seabed is very large, sea water advanced 100 meters of Fig. 2 emulation, 10 meters of depth of stratums, the velocity of sound 1500 meter per seconds in the water, the stratum velocity of sound 1550 meter per seconds, the velocity of sound of simulation actual formation echo is respectively 1500 meter per seconds, 1550 meter per seconds, 1600 meter per seconds, 1650 meter per seconds, a point target echo carries out beam pattern after the synthetic aperture processing, and (horizontal ordinate is for walking to navigate direction length, ordinate is the beam wave beam output valve after synthesizing), the analysis showed that, when needing the control sound velocity error in 6.4% scope, could be so that synthetic aperture processing processing impact be very little.

For this reason in carrying out synthetic aperture stratum chromatography process, need to use different acoustic velocity values according to the different sonic velocity change of echo data and carry out synthetic aperture processing, can be similar to for the seawater data and to think the c=1500 meter per second, and for the seabed data, great changes have taken place for the different stratified medium velocities of sound, but for shallow stratum (30 meters scopes in) sonic velocity change generally in 1550～1650 meter per seconds, get its mean value c=1600 meter per second, then sound velocity error is in 6.4% scope, and it is very little that Technologies Against Synthetic Aperture is processed impact.We need to separate seawater data in the echo of stratum with the seabed data for this reason, it is used different acoustic velocity values carry out synthetic aperture processing.。

● follow the tracks of and process seawater, seabed data separating at the end

Obtain after the matched filtering data energy and integration in short-term

$\mathrm{Ess}(m,n)=\frac{1}{J}\underset{j=1}{\overset{J}{\mathrm{\&Sigma;}}}\left|\mathrm{ss}(m,n+j)\right|---\left(4\right)$

$\mathrm{EEss}\left(m\right)=\frac{1}{N}\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{Ess}(m,n)---\left(5\right)$

When Ess (m, n) 〉=0.707*EEss (m) declares N _s(θ)=n is the seabed constantly.

● layering synthetic aperture processing flow process

Seawater after separating, the different velocity of sound data of seabed market demand are carried out synthetic aperture stratum chromatography, and flow process as shown in Figure 3.In synthetic aperture processing, the interphase in seawater and seabed can form a fuzzy band near interface owing to para-curve aperture focusing addition reason, and this blurs is with us to suppress by rearmounted normalized

4, the layering two dimension forward direction normalization of following the tracks of the end of based on

The normalization of layering two dimension forward direction has solved three problems, the one, stratum, the seabed echo attenutation of different depth is very fast, the 2nd, can not be too obvious near diplopia in the water in seabed (because synthetic aperture processing form fuzzy band), the 3rd, target and the unification of stratum, seabed are carried out the normalization result and can be shown the orientation dispersed problem in the water.(present technique invention scheme success is processed to combine with multi-beam and is built into the three-dimensional formation tomographic system, below the angle θ that occurs in the formula be result after the multi-beam processing)

● follow the tracks of and process at the end

At first to do oblique distance correction and bottom track to the multi-beam output time series before the normalization of layering two dimension forward direction.The oblique distance correction need to be carried out interpolation and resample, the unified degree of depth that is shown as.Bottom track adopt sliding window in short-term (32 point) average amplitude cross the detection method of thresholding, thresholding is set to 0.707 of (not containing head pulse) mean value on the whole time shaft in corresponding orientation, and the seabed interface position of recording each wave beam.(as far as possible the diplopia above the seabed being summed up in the point that the stratum, seabed).

${\mathrm{Ey}}_{\mathrm{\&theta;}}\left(n\right)=\frac{1}{M}\underset{j=1}{\overset{M}{\mathrm{\&Sigma;}}}{y}_{\mathrm{\&theta;}}(n+j)$ θ＝1:K，n＝1:N-M (6)

${\mathrm{EEy}}_{\mathrm{\&theta;}}=\frac{1}{N}\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{y}_{\mathrm{\&theta;}}\left(n\right)---\left(7\right)$

Work as Ey _θ(n) 〉=0.707*EEy _θDeclare N ₀(θ)=n is the seabed constantly

Ey _θ(n) for after processing through matched filtering processing, layering synthetic aperture processing and multi-beam, the energy sequence value on the θ angle direction.

● the seawater data normalization

(target) image shows that only doing global normalization processes, and makes background global mean value (not containing head pulse) normalization in the water

To 16.Require average background value to calculate twice, statistics does not comprise the point greater than 3 times of mean values last time for the second time.

${\mathrm{ESy}}_{\mathrm{\&theta;}}=\frac{1}{N_0\left(\mathrm{\&theta;}\right)}\underset{n=1}{\overset{N_0\left(\mathrm{\&theta;}\right)}{\mathrm{\&Sigma;}}}{y}_{\mathrm{\&theta;}}\left(n\right)---\left(8\right)$

$\mathrm{ESy}=\frac{1}{K}\underset{\mathrm{\&theta;}=1}{\overset{K}{\mathrm{\&Sigma;}}}{\mathrm{ESy}}_{\mathrm{\&theta;}}---\left(9\right)$

K is the beam data that comprises effective seawater data.

y _θ' (n)=y _θ(n) work as y _θ' (n) 〉=3*ESy y _θ' (n)=ESy (10)

${\mathrm{ESy}}^{\&prime;}=\frac{1}{K}\underset{\mathrm{\&theta;}=1}{\overset{K}{\mathrm{\&Sigma;}}}\frac{1}{N_0\left(\mathrm{\&theta;}\right)}\underset{n=1}{\overset{N_0\left(\mathrm{\&theta;}\right)}{\mathrm{\&Sigma;}}}{y_{\mathrm{\&theta;}}}^{\&prime;}\left(n\right)---\left(11\right)$

y _θ′(n)＝y _θ(n)/ESy′*16n≤N ₀(θ)(12)

● the seabed data normalization

The normalization of different azimuth bottom reverberation is got 1/2 power of reverberation intensity mean value on stratum, whole seabed, this orientation as normalized factor.

$\mathrm{EDy}\left(\mathrm{\&theta;}\right)=\frac{1}{N-N_0\left(\mathrm{\&theta;}\right)}\underset{n=1}{\overset{N-N_0\left(\mathrm{\&theta;}\right)}{\mathrm{\&Sigma;}}}{y}_{\mathrm{\&theta;}}\left(n\right)---\left(13\right)$

y′ _θ(n)＝y _θ(n)/sqrt(EDy(θ))n≥N ₀(θ)(14)

The stratum, seabed shows adopts at the same time normalized factor to the different azimuth wave beam, in short-term (32 point) that calculates on each orientation time shaft is average, carry out again the orientation statistical average of orientation normalized factor weighting, adopt 1/2 power of mean value as normalized factor.Closely locate to average by the actual beam number.

$\mathrm{EDy}\left(n\right)=\frac{1}{K\left(n\right)}\underset{\mathrm{\&theta;}=1}{\overset{K\left(n\right)}{\mathrm{\&Sigma;}}}{\mathrm{Ey}}_{\mathrm{\&theta;}}\left(n\right)/\mathrm{sqrt}\left(\mathrm{EDy}\left(\mathrm{\&theta;}\right)\right)---\left(15\right)$

y″ _θ(n)＝y _θ′(n)/sqrt(EDy(n-5))n≥N ₀(θ)(16)

Finally stratum, seabed mean value normalizes to 64 before the amplification quantity effect.

${\mathrm{EEy}}^{\&prime;\&prime;}=\frac{1}{K}\underset{\mathrm{\&theta;}=1}{\overset{K}{\mathrm{\&Sigma;}}}\frac{1}{N-N_0\left(\mathrm{\&theta;}\right)}\underset{n=N_0\left(\mathrm{\&theta;}\right)}{\overset{N}{\mathrm{\&Sigma;}}}{y_{\mathrm{\&theta;}}}^{\&prime;\&prime;}\left(n\right)---\left(17\right)$

y″′ _θ(n)＝y _θ″(n)/EEy″*64n≥N ₀(θ)(18)

5. the extra large test result of stratum, seabed chromatography

Present technique invention combines with multibeam technique and can make up three-dimensional seabed formation imaging system, Fig. 4, Fig. 5 are that present technique invention is applied to three-dimensional seabed formation imaging system, in in October, 2010 to the galore layer region in sea area, Zhoushan with bury the thunder target area and carried out formation imaging detection test result, the present technique invention has acquisition and analyses layer by layer well effect as seen from the figure.

Should illustrate that at last above example is only in order to illustrating technical scheme of the present invention and not limit therewith, but on using, can extend to other modification, change, use, and think the modification that all are such, change, use, embodiment all within the spirit and scope of the present invention.

Claims (3)

1. synthetic aperture stratum chromatography method is characterized in that: comprise that step is as follows:

(1), obtain the stratum echoed signal: launch the broad band low frequency signal, adopting the linear FM signal bandwidth is 1～15kHz, and the layering interfaces reflection echo of acquisition carries out processing by the full frequency band matched filtering;

(2), synthetic aperture stratum chromatography: adopt the vertically downward working method of broad beam transmitting/receiving of acoustic matrix, for stratum echo synthetic aperture processing, synchronization receives the echo of the arc-wave front of a solid, adopts conventional synthetic aperture algorithm to carry out the synthetic aperture focusing wave beam at signal processing method and forms processing;

(3), layering synthetic aperture processing: use the end tracking echo data is divided into two parts of seawater and seabed, then according to seawater, acoustic velocity value that the seabed market demand is corresponding are carried out synthetic aperture processing;

(4), carry out respectively normalized for seawater, seabed, namely carry out rearmounted processing of layering two dimension forward direction normalization on the basis of synthetic aperture processing;

Seawater data in the echo of stratum are separated with the seabed data, it is used different acoustic velocity values carry out synthetic aperture processing;

● follow the tracks of and process seawater, seabed data separating at the end:

Obtain after the matched filtering data energy and integration in short-term

$\mathrm{Ess}(m,n)=\frac{1}{J}\underset{j=1}{\overset{J}{\mathrm{\&Sigma;}}}\left|\mathrm{ss}(m,n+j)\right|---\left(4\right)$

$\mathrm{EEss}\left(m\right)=\frac{1}{N}\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{Ess}(m,n)---\left(5\right)$

When Ess (m, n) 〉=0.707*EEss (m) declares N _s(θ)=n is the seabed constantly;

● the layering synthetic aperture processing:

Seawater after separating, the different velocity of sound data of seabed market demand are carried out synthetic aperture stratum chromatography, in synthetic aperture processing, form a fuzzy band near the interphase in seawater and seabed, this fuzzy band is by rearmounted normalized;

M wherein, n represent to walk respectively boat dimension sample point and depth dimension sample point, and ss (m, n) is energy datum after the matched filtering.

2. synthetic aperture according to claim 1 stratum chromatography method, it is characterized in that: adopt the combined transmit transducer, adopt the sequential firing mode: one group of transducer is launched first the LFM signal of 1kHz-5kHz, accounts for 1/3 of total pulsewidth launch time; And then the LFM signal of another group transducer emission 5kHz-15kHz accounts for 2/3 of total pulsewidth launch time.

3. synthetic aperture according to claim 1 stratum chromatography method is characterized in that: be adopted as time delay focused synthetic aperture disposal route, namely data after the matched filtering represented ss (n with discrete form, m), m, n represent to walk respectively boat dimension sample point and depth dimension sample point m=1,2 ... M; N=1,2 ... N, then image output

$\mathrm{ff}(n,m)=\underset{i=1}{\overset{L_{\mathrm{SA}}}{\mathrm{\&Sigma;}}}\mathrm{ss}(n+\mathrm{\&tau;}(n,i),m+i)---\left(2\right)$

L in the formula _SAFor the orientation to length of synthetic aperture, τ (i, n) is defined as the Delay Variation amount that the range migration curve causes

$\mathrm{\&tau;}(n,i)=\sqrt{n^2+[{2f}_s\&CenterDot;i\&CenterDot;d/c]}-n,$ i=1,2,…L _SA (3)

Wherein d is that spacing is adopted in the space, and c is the velocity of sound, and [] expression rounds operation, carries out sample interpolation operation, f for obtaining accurate delay in processing _sBe sample frequency.

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